| This thesis focuses on the application of feedback control theory to the study of data communication over the Internet. At the heart of this communication lies the transmission control protocol (TCP) which is responsible for reliable and efficient data transfer. Using recently developed fluid models of TCP, we treat its congestion control phase as a feedback system and, through analysis, provide insight on its performance. The contribution of the thesis is twofold. First, it introduces a matrix analysis tool, the matrix field of values, to the stability analysis of congested networks involving arbitrary numbers of heterogeneous TCP-controlled sources and congested links. This tool enables us to derive stability results for buffer-based active queue management (AQM) schemes, revealing the impact that routing plays on stability robustness. This matrix field of values also proves valuable in synthesizing stabilizing source controllers when one considers the possibility of TCP sources sending data over multiple paths. The second contribution of the thesis is to study the scenario where the fluid models predict congestion-control instability and hence predicts that the average behavior of TCP traffic is oscillatory. Using the theory of "weakly-coupled oscillators," we formulate a network problem wherein oscillating traffic from multiple sources traverses a core congested link, and analyze the impact that packet loss at this core link has on the "synchronization" between the oscillating sources. This formulation allows one to then make connection between traffic throughput and the mechanisms contributing to packet loss, such as the congested router's buffer size. |
